The function f(x)=x^2. The graph of g(x) is f(x) translated to the right 3 units and down 3 units. What is the function rule for g(x)?
helpp pleasee
f ( x ) = x²
f ( x ) :
- to the left 8 units: f ( x + 8 )
- to the left 8 units and up 2 units : f ( x + 8 ) + 2 = g ( x )
g ( x ) = ( x + 8 )² + 2
To find the function rule for g(x), which is the graph of f(x) translated right 3 units and down 3 units, we can follow these steps:
1. Start with the original function f(x) = x^2.
2. To translate it to the right 3 units, we need to subtract 3 from x inside the function: f(x-3).
3. To translate it down 3 units, we need to subtract 3 from f(x-3): f(x-3) - 3.
4. Therefore, the function rule for g(x) is: g(x) = f(x-3) - 3.
So, the function rule for g(x) is g(x) = (x-3)^2 - 3.